1728
Anal. Chem. 1983, 55, 1728-1731
conditions remaining constant. SUMMARY We call into question the techniques in the literature which employ least-squares procedures to estimate the mole fractions of species believed to be present. The most serious difficulties with least squares is the lack of statistical independence in the random errors, failure of homoscedasticity, and exact linear dependencies in the observed data which give rise to a singular covariance matrix of the error vector. We applied the Bayesian formalisim of Box and Draper (7) to estimate the mole fractions, the approaches of McLean et al. (12)and Box et al. (7) to eliminate the linear dependencies in the observed data, and some approximations given by Stewart and Srarensen (13,14), and we were able to use formulas given by Box and Tiao (15)for a linear, single response model, to find approximate HPD contours and confidence intervals for the mole fractions. The Bayesian confidence intervals are narrower than those obtained from the leastsquares analysis. All of our applications involved the deconvolution of overlapping spectra resulting from successive loss of hydrogen and, in some cases, gain of hydrogen via ion/molecule reactions. In these examples we emphasized how to interpret the information obtained from the statistical analysis, and we pointed out numerical problems which may force reduction of the assumed model to one involving fewer species. It must be stressed that the statistical method presented may well reject species that an experienced mass spectroscopist would think are present. However, if a species is rejected statistically, one may still wish to claim the existence of it,
perhaps verified by exact mass measurement, but one certainly cannot quantify such a low abundance species based on simple low resolution data. We are indebted to the referees for alerting us to the Bayesian approach for the analysis of multiresponse data and for their valuable comments which facilitated the writing of this paper. LITERATURE C I T E D Clark, Hayden A.; Jurs, Peter C. Anal. Chlm. Acta 1981, 132, 75-88. Benz, Wolfgang Anal. Chem. 1980, 5 2 , 248-252. Blackburn, James A. Anal. Chem. 1985, 3 7 , 1000-1003. Brauman, John I.Anal. Chem. 1968, 38, 607-610. Eakman, J. M. Ind. Eng. Chem. Fundam. 1969, 8 , 53-58. (6) Erjavec, J. Ind. Eng. Chem. Fundam. 1970, 9 , 187. (7) Box, G. E. P.; Hunter, W. G.; MacGregor, J. F.; Erjavec, J. Technome trics 1973, 15, 33-51. (8) Andrews, Mark A.; Klrtley, Stephen W.; Kaesz, Herbert D. Adv. Chem. Ser. 1988, No. 167, 215-231. (9) Hamilton, Waiter Clark "Statistics in Physical Science"; Roland Press: New York, 1964; Chapter 4. (IO) Hamilton, Walter Clark Acta Crystallogr. 1985, 18, 502-510. (1 1) Box, George E. P.; Draper, Norman R. Biometrika 1965, 52, 355-365. (12) McLean, D. D.; Pritchard, D. J.; Bacon, D. W.; Bownle, J. Technometrics 1979, 2 1 , 291-298. (13) Stewart, Warren E.; Serensen, Jan P. Technometrics 1981, 2 3 , 131-141. (14) Stewart, Warren E.; Serensen, Jan P. "Sensltivity and Regression of Multicomponent Reactor Models", I n Fourth International Symposlum on Chemical Reactlon Englneering, Frankfurt; DECHEMA, 1-12-1-20. (15) Box, George, E. P.; Tlao, George C. "Bayeslan Inference In Statlstlcal Analysis"; Addison-Wesley: Reading, MA, 1973; Chapter 2. (16) International Mathematical and Statistical Librarles, Inc. IMSL, Houston, TX, 1980, Version 8. (17) Box, M. J. Compur. J . 1986, 9 , 67-77. (18) Powell, M. J. D. Compur. J . 1984, 7 , 155-162. (1) (2) (3) (4) (5)
RECEIVED for review August 10, 1982. Resubmitted and accepted May 2, 1983.
Oscillometric Flow Cell for Measurement of Conductivity and Permittivity Ern0 Pungor,* Ferenc PB1, and Klhra T d t h Institute for General and Analytical Chemistry, Technical University, Budapest, Hungary
Thls paper reports on a new flow-through oscillornetrlc hlghfrequency conductance mlcrocell which Is sultable for the measurement of conductlvlty or permittivity of streamlng solutions or solvents. The electrodes of the cell are not contacting galvanlcally the measuring solutlon; thus a good stabllity of the electrode surface layer and consequently good reproduclblllty of the measurements can be ensured. The volume of the concentrlc flow cell can vary between 10 and 50 pL.
The increasing demand for monitoring industrial processes and for handling a great number of samples of similar composition in different fields of chemical analysis promoted the development of flow-through measuring techniques. Consequently, a series of continuous flow methods, like flow-injection and flow-titration techniques, were developed. Furthermore, the extended use of different chromatographic methods was significant due to the development of high-pressure liquid chromatography and ion chromatography.
One of the important problems in flow-through measuring techniques is the selection of the appropriate detector. The universal detectors like conductometric detectors can be used primarily in measuring techniques which are combined with either selective chemical treatment as, e.g., in flow titrations, or separations, like various liquid chromatographic methods. Conductometric and permittivity detectors have already been applied to liquid chromatography. With these cells small cell volume ( 1 4 , high sensitivity (6, 7), and wide range of linearity are requirements. In respect of the development of conductivity detectors for ion chromatography the papers presented by Evans et al. (8)and Jupille et al. (9) at the 1982 Pittsburgh Conference and the work of Keller (10) are especially noteworthy. Flow-through permittivity detectors for chromatographic purposes have been designed and studied by several authors (11-18) but more recently great progress has made by Alder et al. (19-21). It appears that in all conductometric and permittivity detectors developed so far there is a direct galvanic contact between the electrodes and the solution tested.
0003-2700/83/0355-1728$01.50/00 1983 Amerlcan Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 55, NO. 11, SEPTEMBER 1983
1729
CS
--I -3
I
-3 -4 ' 5
Figure 2.
Equivalent circuit of a condenser type measuring cell.
Table I. Technical Data of the Cells Applied -2.
working volume, pL 12.0 19.5 39.0
I
Flgure 1. Scheme of the aeil applled: (1) cell body, (2) fixlng screw, (3) Teflon seallng, (4) grounding electrode, (5) measuring electrode, (6)
limit of detection, KCI
-
mol/L
g
2x 1.5 X lo-' 1.6'X
1.8 x 10-9 2.2 x 10-9 4.7 x 10-9
cell outlet. The oscillometric (high frequency conductance) measuring principle (22-24), however, offers a possibility for measuring conductance and permittivity data with cells in which the electrodes are not in gallvanic contact with the solution to be investigated. Thus, errors present in ordinary conductometric or permittivity measuring cells caused by polarization, corrosion, and other side effects, which may clhange the measuring electrode surface condition as well as the cell constant, are eliminated. The aim of the present work was to devlelop an oscillometric high-frequency conductance flow cell in vvhich the measuring electrodes are completely isolated from the sample solution; thus, the electrodes arc?not in galvanic contact with the solution tested and its cell volume is adapted t~ the requirements of chromatographers. At its present stage the cell is coupled to a Hungarian made oscillotitrator, but it can be used with every type of oscillometer system available.
EXPERIMENTAL SEC'I'ION In the course of the present work, different types of cells have been designed and studied, among which t b e one shown in Figure 1 was found the best. It has a concentric cell design, thus the effect of stray capacitance has decreased. The electrodes of this cell were made of bpass and their surfaces were coated with a silicone lacquer or Teflon layer. The silicone coating was prepared by immersing the electrodes in silicon resin dissolved in a mixture of xylene-cyclohexaniol-acetone (9:1:20 vol ratio) and then dried and baked. (A clean and greaseless surface is required for the appropriate coating layer.) Teflon rings filled up the dead volumes existing between the electrodes and the cell body. The cell body was made of Perspex or Teflon. The sample solution is led to the cell by means of Teflon tubes. The cell volume is changed by altering the electrode sizeg. The measurements were carried out with m oscillotitrator (type OK-302/1, Radelkis, Hungary) coupled with a condenser type cell. (The operating frequency of the instrument was 42 MHz and it had an analog output (0-4 V). The signal (instrumental reading) of the instrument is inversely proportional to the conductance of the sample.) The solution was streamed by a peristaltic pump (Varioperpex type 12000, LKB, Sweden). The signal was recorded with a potentiometric recorder (type OH 814/1, Radelkis, Hungary). In special cases the cell was supplied with an injector valve (type OE-320, Labor MIM, Hungary). For conductivity meariurements the cells were calibrated with KC1 solutions of different concentrations. KCl solutions were prepared by diluting 0.1 mol/L KC1 with degassed twice-distilled water (the specific conductivity of twice distilled water, K = 1.5-2.5 pS depending on storagie). The solutions were stored in plastic bottles. At the beginning of the measurements the cells were filled up bubble free with twice-distilled water. It was advantageous to operate the cell under an over pressure (about 80 cm of water)
to avoid bubble formation and its consequence, the "bubble noise". For permittivity studies, the same type of cell was used as shown in Figure 1, with the modification that the cell body was made of Teflon. The cell was calibrated with solvents of different permittivities, e.g., dioxanewater mixtures, n-pentane, n-hexane, cyclohexane, CC4, benzene. The oscillometric detector has been used for flow-injection studies. Twice distilled water was used as a carrier solution for conductivity measurement, while for permittivity studies a 30 vol % water-dioxane mixture was used. The flow rate of the carrier stream was 2.5 mL/min. The test solution injected was, in the former case, potassium chloride solution and, in the latter, glucose dissolved in 30 vol % water-dioxane solvent mixture. The sample volume injected was in all cases 20 pL.
RESULTS AND DISCUSSION The conductance, K, of a condenser type cell with the equivalent electrical circuit presented in Figure 2 is
where w is the measuring frequency (w = 27rf), Hz,R is the solution resistance, Q,C, is the stray capacitance, F, E is the permittivity, and C M ,is~ the cell capacitance, F. If the second term in the denominator of eq 1 is small compared to unity, then it can be neglected and the conductance becomes a linear function of the solution resistance. Furthermore, eq 1 can be simplified if C, is negligible compared to ECM,~ and if the second term in the denominator is high compared to unity. Then
K = - c,2 R e2CM,02
(2)
and
(3) Thus one can measure the solution permittivity as a function of the square root of the ac conductance if the value of R is relatively high and constant. From the above it follows that theoretically an oscillometric detector system can be appropriate either for permittivity measurements, if the solution conductivity is small, or for conductivity measurements, if the solution conductivity is high. In conductivity measurements the calibration curves obtained by passing potassium chloride solutions through the measuring cells were linear in the range 5 X lo4 to 5 X 10" mol/L. The signal was found to be flow-rate independent in the range 20-200 mL/h. The limits of detection with measuring cells of different
ANALYTICAL CHEMISTRY, VOL. 55, NO. 11, SEPTEMBER 1983
1730
Table 11. Data for Solvents Used solvent
€m
yS
instrument deflection
n-pentane n-hexane cyclohexane CCl, dioxane benzene
1.844 1.890 2.023 2.230 2.235 2.283
0.07 0.07 0.07 0.07 0.07 0.07
10.1 11.5 15.1 21.9 22.1 24.0
r;;l--+-w C.
YO 120
/
l n s t r . readings
110
iao 90
80
60
b
a
70 60
50
a ..
40
I
1
c
Flgure 4. Recorder trace obtained with flow-injection technique: flow-rate, 2.5 mL/min; injected volume, 20 pL; injected sample, (a) 5 X mol/L KCI, (b) mol/L KCI, (c) 5 X moVL KCI.
M 20
W
S
1
U
Figure 3. Calibration graph for dioxane-water mixtures as a function of permittivity.
volumes are summarized in Table I. The detection limit was calculated as follows:
2s c, = Y where C, is the detection limit, mol/L, Y is the slope of the calibration curve, instrument reading L/mol, and S is the shift of the base line in 1 h, in instrument reading. The base line drift is due to electronic drift and temperature changes measured in twice distilled water. Since the measurements were carried out at constant temperature, we used for the calculation a value of S = 1 unit/h. Without thermostating, the reproducibility of the signals was between *l% and *3 % . As can be seen from eq 2, the conductance is a function of both solution resistance and the square of solution permittivity. Thus if the solution resistant is constant and relatively high, the permittivity change can be detected through conductance measurements. To test the validity of the correlation, we used the following equation: A ( l / K ) = k.Ae2, where k is the proportionality factor. k = 7.88 f 0.48 was found on the basis of all experimental data shown in Table 11, which proves the validity of our simplifying assumptions. A calibration graph for different dioxane-water mixtures is shown in Figure 3, where, besides the measured points, the corresponding solution conductivities ( K ) are also indicated. In our work we have demonstrated the applicability of the oscillometric detector system for flow-injection studies. Some recordings are shown in Figure 4. The reproducibility of the signal, i.e., peak height, at laboratory temperature without thermostating was fl% at injecting 2 X IO4 mol of KC1 into
W
W
2 rnin
40
b
30 20 IO
0
_i
I \
Flgure 5. Recorder trace obtained with flow-injection technique: flow rate, 2.5 mL/min; injected volume, 20 pL; injected sample, (a) 2 mg of glucose/100 mL, (b) 10 mg of glucose/100 mL, (c) 20 mg of glucose/100 mL.
pure distilled water and about &3% a t the injection of 2 X mol of KC1. Figure 5 presents data for glucose determination by the flow-injection technique. The amount detected was on the order of 100 ng of glucose. On the basis of this work it can be concluded that small volume oscillometric cells are appropriate for measurement of either conductivity or permittivity in streaming solutions or solvents. Thus, it holds promise in flow-injection and chromatographic analyses.
LITERATURE CITED (1) Pecsok, R. L.; Saunders, D. L. Anal. Chem. 1968, 4 0 , 1765. (2) Tesarik, K.; Kallb, P. J . Chromatogr. 1973, 78, 357.
Anal. Chem. 1983,55, 1731-1734 (3) Stankoviansky, S.;Cicrnanec, P.; Kaniansky, D. J. Chromatogr. 1975, 106, 131. (4) Jackson, A. J. Chem. Educ. 1965, 42, 447. (5) Svoboda, V.; Marsai, J. J . Chromatogr. 1978, 148, 111. (6) Kambara, T.; Tachikawa, T. J. Chromatogr. 1968, 3 2 , 728. (7) Duhne, C.; Sancher, 01.Anal. Chem. 1962, 3 4 , 1074. (8) Jupille, T.; Togami, D.; Burger, D. Abstract 242, Pittsburgh Conference, 1982. (9) Evans, B.; Stoiz, J. Abstract 247, Pittsburgh Conference, 1982. (10) Keller, J. M. Anal. Chem. 1981, 5 3 , 344. (11) Haderka, S.J . Chrom,stogr. 1971, 5 7 , 181. (12) Vespalec, R.; Hana, K. J. Chromatogr. 1972, 6 5 , 53. (13) Poppe, H.; Kuysten, J. J . Chromatogr. 1977, 132, 369. (14) Erbelding, W. F. Anal. Chem. 1975, 47, 1983. (15) Krejci, M.; Pospisilova, N. J . Chromatogr. 1972, 7 3 , 105. (16) Vespalec, R. J . Chronoatogr. 1975, 108, 243. (17) Krejci, M.; Vespalec, R.; Sirec, M. J. Chromatogr. 1972, 6 5 , 333.
1731
(18) Haderka, S.J. Chromatogr. 1974, 9 1 , 167. (19) Alder, J. F.; Thoer, A. J. Chromatogr. 1979, 178, 15. (20) Aider, J. F.; Drew, P. K. P.; Fieiden, P. R. J . Chromatogr. 1981, 212, 167. (21) Aider, J. F.; Drew, P. K. P.; Fieiden, P. R. J . Chromatogr. 1983, 5 5 , 256. (22) Pungor, E. "Osciilometry and Conductometry"; Pergamon Press: Oxford, London, Edinburgh, New York, Paris, 1965. (23) Cruse, K.; Huber, R. "Hochfrequenztitration"; Verlag Chemie: Weinheim, 1957. (24) Reilley, Ch. N. "High Frequency Methods In New Instrumental Methods in Electrochemistry"; Deiahey, P., Ed.; Interscience: New York, London, 1954.
RECEIVED for review April 19, 1982. Resubmitted February 8, 1983. Accepted May 10, 1983.
Determination of Total Dissolved Sulfide in the pH Range 7.5 to 11.5 by Ion Selective Electrodes Hugo Guterman andl Sam Ben-Yaakov*
Department of Electrical and Computer Engineering, Ben-Gurion University of the Negeu, Beer-Sheua, Israel Aharon Abeliovich
Laboratory for Environmental Applied Microbiology, The Jacob Blaustein Desert Research Institute, Ben-Gurion University, Sede Boquer Campus 84990, Israel
A total dlssolved sulfldie meter was designed and tested over the concentratlon range to lo-' mol/L. The Instrument applies a sulfide Ion aotivlty electrode and a pH glass electrode, whose potential6 are measured agalnst a double Junctlon reference electrode. The potentials are processed by an electronic analog clrcult to obtaln an output voltage that Is proportional to total dlssolved sulfide. The proposed Instrument-adjustment procedure ellmlnates mutual dependence of the adjusted1 controls. The total dissolved sulfide readings of the Instrument were found to be pH independent over the pH range pH 7.5 to pH 11.5.
This is a rather severe limitation as the pH of most natural waters as well as treated and untreated wastewaters are above this range (1-,3). The purpose of this study was to develop a direct method, based on analog instrumentation, for determination of total sulfide concentration in the pH range above pH 7 applicable for in situ measurements. The present approach differs from the one proposed by Brand and Rechnitz (8)who considered direct differential measurement between two ion selective electrodes such as a pH glass electrode and a sodium ion selective electrode. Their approach, which is similar to the one also suggested by Wilde and Rogers (9), does not allow for total concentration determination when the valencies of the pertinent ions are not identical.
The importance of sillfide compounds in biological processes has been widely demonstrated ( 1 , 2 )and it is well-known that the generation of sulfide is linked to a number of vital, chemical, physical, and biochemical processes (3). The classical analytical methods for sulfide determination like the Methylene Blue or the iodomotric methods (4) are rather cumbersome, requiring elaborate sample handling and preparation and lengtlny calibration. In situ measurement of sulfide activity has bleen made possiblle through the introduction of ion-selective membrane electrodes (4). However, since these electrodes are sensitive to sulfide activity, determination of total sulfide can be accomplished only after the samples are buffered tri high pH by a higlh ionic strength buffer such as SAOB I1 (5). Total sulfide can be calculated from a simultaneous measurement by sulfide and pH electrodes. A suitable microcomputer interface for implementing such an instrumentation system has been recently described by Ben-Yaakov et al. (6). Frevert and Galster (7) proposed an analog method for direct determination of total sulfide by using a sulfide ion selective electrode coupled to a pH glass electrode. This method is limited to solutions with pHs
